interpol.cc 194 KB
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/**********************************************************************************
 * Copyright 2010 Christoph Pflaum 
 * 		Department Informatik Lehrstuhl 10 - Systemsimulation
 *		Friedrich-Alexander Universität Erlangen-Nürnberg
 * 
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 * http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 **********************************************************************************/


#include "../mympi.h"
#include "../abbrevi.h"
#include "../parameter.h"
#include "../math_lib/math_lib.h"
#include "../basics/basic.h"
#include "../grid/elements.h"
#include "../grid/parti.h"
#include "../grid/ug.h"
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#include "../grid/examples_ug.h"
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#include "../grid/blockgrid.h"
#include "../grid/marker.h"
#include "../extemp/extemp.h"
#include "../extemp/parallel.h"
#include "../extemp/variable.h"
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#include "../extemp/cellvar.h"
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#include "../extemp/co_fu.h"
#include "../extemp/functor.h"
#include "interpol.h"
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//#include "customtime.h"
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#include <iomanip>
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#include "assert.h"

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/////////////////////////////////////////////////////////////
// 1. Interpolate from  blockgrid to rectangular blockgrid
/////////////////////////////////////////////////////////////


bool contained_in_tet(D3vector lam) {
  if(lam.x < -0.1)                 return false;
  if(lam.y < -0.1)                 return false;
  if(lam.z < -0.1)                 return false;
  if(lam.x + lam.y + lam.z > 1.1)  return false;
  return true;
}

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bool contained_in_tet_strong(D3vector lam) {
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    double limit = 0.2; // 0.2
  if(lam.x < -limit)                 return false;
  if(lam.y < -limit)                 return false;
  if(lam.z < -limit)                 return false;
  if(lam.x + lam.y + lam.z > 1+limit)  return false;
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  return true;
}
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bool contained_in_tet_direct(D3vector lam) {
    double limit = 0.0; // 0.2
  if(lam.x < -limit)                 return false;
  if(lam.y < -limit)                 return false;
  if(lam.z < -limit)                 return false;
  if(lam.x + lam.y + lam.z > 1+limit)  return false;
  return true;
}
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bool new_lam_better(D3vector lam_old, D3vector lam_new) {

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    if (MIN(lam_new ) < -0.2 || MAX(lam_new) > 1.2) return false;
    if (MIN(lam_old ) < -0.2 || MAX(lam_old) > 1.2) return true;
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    if( (MIN(lam_new ) < 0 || MAX(lam_new) >1 )&&  (MIN(lam_old ) >= 0 || MAX(lam_old) <=1 )) return false;
    if (MIN(lam_new) > MIN(lam_old)) return true;
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    if (MAX(lam_new) < MAX(lam_old)) return true;
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    return false;
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}

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bool new_lam_worse(D3vector lam_old, D3vector lam_new) {
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  if(MIN(lam_new) < MIN(lam_old) &&  MIN(lam_old) < -0.2) return true;
  if(MAX(lam_new) > MAX(lam_old) &&  MAX(lam_old) >  1.2) return true;
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  return false;
}

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/*
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Intermadiate_grid_for_PointInterpolator::Intermadiate_grid_for_PointInterpolator(int nx_, int ny_, int nz_, Variable<double>* U_from)
{
    nx = nx_;
    ny = ny_;
    nz = nz_;
 
    if(nx<=2) nx = 3;
    if(ny<=2) ny = 3;
    if(nz<=2) nz = 3;
     
    Blockgrid* blockgrid_from = U_from->Give_blockgrid();
    
    //Variable<double> coordXYZ(*blockgrid);
    X_coordinate Xc(*blockgrid_from);
    Y_coordinate Yc(*blockgrid_from);
    Z_coordinate Zc(*blockgrid_from);
    pWSD.x = Minimum(Xc);    pWSD.y = Minimum(Yc);    pWSD.z = Minimum(Zc);
    pENT.x = Maximum(Xc);    pENT.y = Maximum(Yc);    pENT.z = Maximum(Zc);  
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    interpolatorStructured = new Interpolate_on_structured_grid(nx,ny,nz, pWSD, pENT, *blockgrid_from);
    
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}
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*/
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Interpolate_on_structured_grid::~Interpolate_on_structured_grid() {
  delete[] ids_hex;
  delete[] ids_i;
  delete[] ids_j;
  delete[] ids_k;

  delete[] typ_tet;
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    delete[] lambda;
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}
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void Interpolate_on_structured_grid::update_Interpolate_on_structured_grid(Blockgrid &blockgrid_, bool onlyOnSurfaceZ)
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{
        int Nx, Ny, Nz;
        int typ;

        int ilmin, jlmin, klmin;
        int ilmax, jlmax, klmax;

        double factor = 0.1;
        //  double factor = 0.00001;

        D3vector lam;


          //Variable<double> coordXYZ(*blockgrid);
          X_coordinate Xc(blockgrid_);
          Y_coordinate Yc(blockgrid_);
          Z_coordinate Zc(blockgrid_);
          //D3vector pWSD, pENT;
          pWSD.x = Minimum(Xc);    pWSD.y = Minimum(Yc);    pWSD.z = Minimum(Zc);
          pENT.x = Maximum(Xc);    pENT.y = Maximum(Yc);    pENT.z = Maximum(Zc);

        blockgrid = &blockgrid_;
        ug = blockgrid->Give_unstructured_grid();



        if(nx>1)
          hx = (pENT.x - pWSD.x) / (nx-1);
        else
          hx = 1.0;
        if(ny>1)
          hy = (pENT.y - pWSD.y) / (ny-1);
        else
          hy = 1.0;
        if(nz>1)
          hz = (pENT.z - pWSD.z) / (nz-1);
        else
          hz = 1.0;

        int num_total = nx * ny * nz;

        D3vector cWSD, cESD;
        D3vector cWND, cEND;

        D3vector cWST, cEST;
        D3vector cWNT, cENT;

        D3vector boxWSD, boxENT;

        D3vector ploc;





        for(int i=0;i<num_total;++i) ids_hex[i] = -1;

        for(int id_hex=0;id_hex<ug->Give_number_hexahedra();++id_hex) {
            Nx = blockgrid->Give_Nx_hexahedron(id_hex);
            Ny = blockgrid->Give_Ny_hexahedron(id_hex);
            Nz = blockgrid->Give_Nz_hexahedron(id_hex);

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            int limitForZ = Nz;
            if (onlyOnSurfaceZ)
            {limitForZ = 1;}

          for(int k=0;k<limitForZ;++k)
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          for(int j=0;j<Ny;++j)
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            for(int i=0;i<Nx;++i)
            //if (k == 0 || k == (Nz-1) || j == 0 || j == (Ny-1) || i == 0 || i == (Nx-1))
            {
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                  // corner points of general hex-cell
              cWSD = blockgrid->Give_coord_hexahedron(id_hex,i,  j,  k  );
              cESD = blockgrid->Give_coord_hexahedron(id_hex,i+1,j  ,k  );
              cWND = blockgrid->Give_coord_hexahedron(id_hex,i,  j+1,k  );
              cEND = blockgrid->Give_coord_hexahedron(id_hex,i+1,j+1,k  );

              cWST = blockgrid->Give_coord_hexahedron(id_hex,i,  j,  k+1);
              cEST = blockgrid->Give_coord_hexahedron(id_hex,i+1,j  ,k+1);
              cWNT = blockgrid->Give_coord_hexahedron(id_hex,i,  j+1,k+1);
              cENT = blockgrid->Give_coord_hexahedron(id_hex,i+1,j+1,k+1);

                  // bounding box calculation
              boxWSD.x = MIN(MIN(MIN(cWSD.x,cESD.x),MIN(cWND.x,cEND.x)),
                     MIN(MIN(cWST.x,cEST.x),MIN(cWNT.x,cENT.x))) - factor *hx;
              boxWSD.y = MIN(MIN(MIN(cWSD.y,cESD.y),MIN(cWND.y,cEND.y)),
                     MIN(MIN(cWST.y,cEST.y),MIN(cWNT.y,cENT.y))) - factor *hy;
              boxWSD.z = MIN(MIN(MIN(cWSD.z,cESD.z),MIN(cWND.z,cEND.z)),
                     MIN(MIN(cWST.z,cEST.z),MIN(cWNT.z,cENT.z))) - factor *hz;

              boxENT.x = MAX(MAX(MAX(cWSD.x,cESD.x),MAX(cWND.x,cEND.x)),
                     MAX(MAX(cWST.x,cEST.x),MAX(cWNT.x,cENT.x))) + factor *hx;
              boxENT.y = MAX(MAX(MAX(cWSD.y,cESD.y),MAX(cWND.y,cEND.y)),
                     MAX(MAX(cWST.y,cEST.y),MAX(cWNT.y,cENT.y))) + factor *hy;
              boxENT.z = MAX(MAX(MAX(cWSD.z,cESD.z),MAX(cWND.z,cEND.z)),
                     MAX(MAX(cWST.z,cEST.z),MAX(cWNT.z,cENT.z))) + factor *hz;

              // calculation of indices of a collection of cells of structured grid which contains bounding box
              ilmin = Ganzzahliger_Anteil((boxWSD.x - pWSD.x) / hx);
              jlmin = Ganzzahliger_Anteil((boxWSD.y - pWSD.y) / hy);
              klmin = Ganzzahliger_Anteil((boxWSD.z - pWSD.z) / hz);


              ilmax = Ganzzahliger_Anteil((boxENT.x - pWSD.x) / hx);
              jlmax = Ganzzahliger_Anteil((boxENT.y - pWSD.y) / hy);
              klmax = Ganzzahliger_Anteil((boxENT.z - pWSD.z) / hz);

              /*
              cout << " indices: "
               << " ilmin: " << ilmin
               << " jlmin: " << jlmin
               << " klmin: " << klmin
               << " ilmax: " << ilmax
               << " jlmax: " << jlmax
               << " klmax: " << klmax
               << " boxWSD.x: " << boxWSD.x
               << " cWSD.x: " << cWSD.x
               << " Nx: " <<  Nx
               << endl;
              */
              /*
      bool now;
      if(boxWSD.z < 0 && boxENT.z > 0.0 && boxWSD.y < 0.5 && boxENT.y > 0.5 && boxWSD.x < 1.0 && boxENT.x > 1.0 ) {
        cout << "\n \n WSD   : ";  boxWSD.Print();
        cout << "\n ENT  : ";  boxENT.Print();
        now = true;
       }
       else now = false;


       cout << " tt: " << boxWSD.x << " " << pWSD.x << " " << hx << endl;
       cout << (boxWSD.x - pWSD.x) << endl;

       cout << " z: " << 0.1 << " g: " << Ganzzahliger_Anteil(0.1) << endl;
       cout << " z: " << -0.1 << " g: " << Ganzzahliger_Anteil(-0.1) << endl;

       cout << " z: " << 5.1 << " g: " << Ganzzahliger_Anteil(5.1) << endl;
       cout << " z: " << -5.1 << " g: " << Ganzzahliger_Anteil(-5.1) << endl;
              */

              if(ilmin<0) ilmin=0;
              if(jlmin<0) jlmin=0;
              if(klmin<0) klmin=0;

              for(int il = ilmin; (il <= ilmax) && (il < nx);++il)
                for(int jl = jlmin; (jl <= jlmax) && (jl < ny);++jl)
              for(int kl = klmin; (kl <= klmax) && (kl < nz);++kl) {

                ploc = D3vector(il * hx, jl * hy, kl * hz) + pWSD;

                //		  cout << "HI" << endl;

                typ = -1;

                lam = lambda_of_p_in_tet(ploc,cWND,cWNT,cWST,cEST);
                if(contained_in_tet(lam)) typ=0;
                else {
                  lam = lambda_of_p_in_tet(ploc,cEST,cWND,cWST,cESD);
                  if(contained_in_tet(lam)) typ=1;
                  else {
                    lam = lambda_of_p_in_tet(ploc,cWND,cWSD,cWST,cESD);
                    if(contained_in_tet(lam)) typ=2;
                    else {
                  lam = lambda_of_p_in_tet(ploc,cEST,cWND,cESD,cEND);
                  if(contained_in_tet(lam)) typ=3;
                  else {
                    lam = lambda_of_p_in_tet(ploc,cENT,cWNT,cEST,cEND);
                    if(contained_in_tet(lam)) typ=4;
                    else {
                      lam = lambda_of_p_in_tet(ploc,cWNT,cWND,cEST,cEND);
                      if(contained_in_tet(lam)) typ=5;
                    }
                  }
                    }
                  }
                }
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                if (trilinearInterpolationFlag && MIN(lam)>= 0.0 && MAX(lam) <= 1.0 )
                {
                    lam = trilinarInterpolation(ploc, id_hex,i,  j,  k);
                    typ = 6;
                }
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                /*
                cout << " typ " << typ << id_hex
                     << " il: " << il
                     << " jl: " << jl
                     << " kl: " << kl
                     << endl;
                */

                if(typ!=-1) {
                  int ind_global;
                  ind_global = il+nx*(jl+ny*kl);
                  bool stop;
                  stop=false;

                  if(ids_hex[ind_global]!=-1) {
                    stop=new_lam_worse(lambda[ind_global],lam);
                  }

                  if(stop==false) {
                    ids_hex[ind_global] = id_hex;
                    ids_i[ind_global] = i;
                    ids_j[ind_global] = j;
                    ids_k[ind_global] = k;

                    typ_tet[ind_global] = typ;

                    lambda[ind_global] = lam;
                  }
                  //go_on = false;
                }


              }
            }
        }


        for(int i=0;i<num_total;++i) {
          if(ids_hex[i]==-1) {
            // wir nehmen default value!!
            /*
            cout << i
             << " Error: Interpolate_on_structured_grid: I cannot interpolate all data!"
             << endl;
            ids_hex[i] = 0;
            */
          }
          else {
            //cout << i << " Interpolate_on_structured_grid: o.k.!" << endl;
          }
        }
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}

D3vector Interpolate_on_structured_grid::trilinarInterpolation(D3vector X, int id_Hex, int i, int j, int k)
{
    D3vector cWSD = blockgrid->Give_coord_hexahedron(id_Hex,i,  j,  k  );
    D3vector cESD = blockgrid->Give_coord_hexahedron(id_Hex,i+1,j  ,k  );
    D3vector cWND = blockgrid->Give_coord_hexahedron(id_Hex,i,  j+1,k  );
    D3vector cEND = blockgrid->Give_coord_hexahedron(id_Hex,i+1,j+1,k  );

    D3vector cWST = blockgrid->Give_coord_hexahedron(id_Hex,i,  j,  k+1);
    D3vector cEST = blockgrid->Give_coord_hexahedron(id_Hex,i+1,j  ,k+1);
    D3vector cWNT = blockgrid->Give_coord_hexahedron(id_Hex,i,  j+1,k+1);
    D3vector cENT = blockgrid->Give_coord_hexahedron(id_Hex,i+1,j+1,k+1);

    D3vector B = cESD - cEND; // 100 - 000
    D3vector C = cWND - cEND; // 010 - 000
    D3vector D = cENT - cEND; // 001 - 000
    //std::cout << "to be implemented" << std::endl;


//    X = (cWSD+ cESD+ cWND + cEND + cWST + cEST + cWNT + cENT   ) / 8.0 ;

//    X.x = X.x +15;
//    X.y = X.y +15;
    D3vector normalTD = cross_product(-1*B,C);
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    D3vector normalTDOPP = -1*cross_product(cWST-cEST , cWNT - cWST);
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    //D3vector normalTDOPP2 = cross_product(cENT-cEST ,cWNT - cENT);
    D3vector normalNS = cross_product(-1*C,D);
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    D3vector normalNSOPP = -1*cross_product(cWST-cEST,cWST - cWSD);
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    //D3vector normalNSOPP2 = cross_product(cESD-cEST,cESD - cWSD);
    D3vector normalEW = cross_product(-1*D,B);
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    D3vector normalEWOPP = -1*cross_product(cWST-cWSD,cWST - cWNT);
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    //D3vector normalEWOPP2 = cross_product(cWND-cWSD,cWND - cWNT);
    normalTD = normalTD / D3VectorNorm(normalTD);
    normalTDOPP = normalTDOPP / D3VectorNorm(normalTDOPP);
    normalNS = normalNS / D3VectorNorm(normalNS);
    normalNSOPP = normalNSOPP / D3VectorNorm(normalNSOPP);
    normalEW = normalEW / D3VectorNorm(normalEW);
    normalEWOPP = normalEWOPP / D3VectorNorm(normalEWOPP);
    double eta = 0.5;
    double xi  = 0.5;
    double phi = 0.5;
    bool fixEta = false;
    bool fixXi = false;
    bool fixPhi = false;
    D3vector coord(eta,xi,phi);

    double distTD0 = product(normalTD,cEND);
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    double TEST1 = product(normalTD,cWND);
    double TEST2 = product(normalTD,cESD);
    double TEST3 = product(normalTD,cWSD);
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    double distTD1 = product(normalTDOPP,cWST);
    double distTDMid  = distTD0-product(normalTD,X);
    double distTDMid2 = distTD1-product(normalTDOPP,X);

    double distNS0 = product(normalNS,cEND);
    double distNS1 = product(normalNSOPP,cWST);
    double distNSMid = distNS0-product(normalNS,X);
    double distNSMid2 = distNS1 -product(normalNSOPP,X);

    double distEW0 = product(normalEW,cEND);
    double distEW1 = product(normalEWOPP,cWST);
    double distEWMid = distEW0-product(normalEW,X);
    double distEWMid2 = distEW1 -product(normalEWOPP,X);


//    std::cout << "in range " << isInRange(distTDMid,distTDMid2) << std::endl;
//    std::cout << "in range " << isInRange(distNSMid,distNSMid2) << std::endl;
//    std::cout << "in range " << isInRange(distEWMid,distEWMid2) << std::endl;

//    if (!isInRange(distTDMid,distTDMid2) || !isInRange(distNSMid,distNSMid2) || !isInRange(distEWMid,distEWMid2) )
//    {
//        return D3vector{-1,-1,-1};
//    }
//    std::cout << "in range " << isInRange(distTDMid,distTDMid2) << std::endl;
//    std::cout << "in range " << isInRange(distNSMid,distNSMid2) << std::endl;
//    std::cout << "in range " << isInRange(distEWMid,distEWMid2) << std::endl;

    D3vector A = cEND;        // 000
    D3vector E = cWSD - cESD - cWND + cEND;        // 110 - 100 - 010 + 000
    D3vector F = cWNT - cWND - cENT + cEND;        // 011 - 010 - 001 + 000
    D3vector G = cEST - cESD - cENT + cEND;        // 101 - 100 - 001 + 000
    D3vector H = cWST + cESD + cWND + cENT - cEND - cWSD - cWNT - cEST;        // 111 + 100 + 010 + 001 - 000 - 110 - 011 - 101
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    if (fabs(angle_between_vectors(normalTD,normalTDOPP)-180*0) < 0.5)
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    {
        double delta = (distTD1 - distTD0);
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        //phi = (distTDMid + delta - distTDMid2) /delta/ 2.0;
        //std::cout << "phi  1 "<< phi << std::endl;
        phi = -distTDMid / delta;
        //std::cout << "phi  2 "<< phi << std::endl;
        //phi = distTDMid2 / delta;
        //std::cout << "phi  3 "<< phi << std::endl;
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        coord.z = phi;
        fixPhi = true;
    }
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    if (fabs(angle_between_vectors(normalNS,normalNSOPP)-180*0) < 0.5)
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    {
        double delta = (distNS1 - distNS0);
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        //eta = (distNSMid + delta - distNSMid2) /delta / 2.0;
        //std::cout << "eta  1 "<< eta << std::endl;
        eta = -distNSMid / delta;
        //std::cout << "eta  2 "<< eta << std::endl;
        //eta = distNSMid2 / delta;
        //std::cout << "eta  3 "<< eta << std::endl;
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        coord.x = eta;
        fixEta = true;
    }
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    if (fabs(angle_between_vectors(normalEW,normalEWOPP)-180*0) < 0.5)
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    {
        double delta = (distEW1 - distEW0);
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        //xi = (distEWMid + delta - distEWMid2) /delta/ 2.0;
        //std::cout << "xi  1 "<< xi << std::endl;
        xi = -distEWMid / delta;
        //std::cout << "xi  2 "<< xi << std::endl;
        //xi = distEWMid2 / delta;
        //std::cout << "xi  3 "<< xi << std::endl;
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        //xi = (distEWMid + distEWMid2)/ 2.0 / (distEW1 - distEW0);
        coord.y = xi;
        fixXi = true;
    }

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//    std::cout << "initial guess\n";
//    coord.Print();std::cout<<std::endl;
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    D3vector R = A    + B * coord.x + C * coord.y + D * coord.z + E * coord.x*coord.y + F * coord.y*coord.z + G * coord.x * coord.z + H * coord.x*coord.y*coord.z;
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    //
//    coord.x = 1; coord.y = 0; coord.z = 0;
//    R = A    + B * coord.x + C * coord.y + D * coord.z + E * coord.x*coord.y + F * coord.y*coord.z + G * coord.x * coord.z + H * coord.x*coord.y*coord.z;
//    R.Print();
//    coord.x = 0; coord.y = 1; coord.z = 0;
//    R = A    + B * coord.x + C * coord.y + D * coord.z + E * coord.x*coord.y + F * coord.y*coord.z + G * coord.x * coord.z + H * coord.x*coord.y*coord.z;
//    R.Print();
//    coord.x = 0; coord.y = 0; coord.z = 1;
//    R = A    + B * coord.x + C * coord.y + D * coord.z + E * coord.x*coord.y + F * coord.y*coord.z + G * coord.x * coord.z + H * coord.x*coord.y*coord.z;
//    R.Print();
//    coord.x = 1; coord.y = 1; coord.z = 0;
//    R = A    + B * coord.x + C * coord.y + D * coord.z + E * coord.x*coord.y + F * coord.y*coord.z + G * coord.x * coord.z + H * coord.x*coord.y*coord.z;
//    R.Print();
//    coord.x = 0; coord.y = 1; coord.z = 1;
//    R = A    + B * coord.x + C * coord.y + D * coord.z + E * coord.x*coord.y + F * coord.y*coord.z + G * coord.x * coord.z + H * coord.x*coord.y*coord.z;
//    R.Print();
//    coord.x = 1; coord.y = 0; coord.z = 1;
//    R = A    + B * coord.x + C * coord.y + D * coord.z + E * coord.x*coord.y + F * coord.y*coord.z + G * coord.x * coord.z + H * coord.x*coord.y*coord.z;
//    R.Print();
//    coord.x = 0; coord.y = 0; coord.z = 0;
//    R = A    + B * coord.x + C * coord.y + D * coord.z + E * coord.x*coord.y + F * coord.y*coord.z + G * coord.x * coord.z + H * coord.x*coord.y*coord.z;
//    R.Print();
//    coord.x = 1; coord.y = 1; coord.z = 1;
//    R = A    + B * coord.x + C * coord.y + D * coord.z + E * coord.x*coord.y + F * coord.y*coord.z + G * coord.x * coord.z + H * coord.x*coord.y*coord.z;
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//    R.Print();std::cout<<std::endl;
//  X.Print();

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D3vector x;
D3vector coordPrev;
        for (int iter = 0 ; iter < 50 ; iter++)
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        {
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            coordPrev = coord;
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            D3vector partialEta = B + E * coord.y + G * coord.z + H * coord.y*coord.z;
            D3vector partialXi =  C + E * coord.x + F * coord.z + H * coord.x*coord.z;
            D3vector partialPhi = D + F * coord.y + G * coord.x + H * coord.x*coord.y;



            D3matrix jac2(partialEta,partialXi,partialPhi);
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            //jac2.transpose();
            //jac2.invert_gauss_elimination();
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            R = A    + B * coord.x + C * coord.y + D * coord.z + E * coord.x*coord.y + F * coord.y*coord.z + G * coord.x * coord.z + H * coord.x*coord.y*coord.z -X;


            //std::cout << "residuum f_xn" <<D3VectorNorm(R)<<std::endl;
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//            if (D3VectorNormSquared(R) < 1e-10)
//            {
//                iter = 1000;
//            }
           // coord.Print(); std::cout << std::flush;
            coord = coord - jac2.invert_apply(R) * 1.0;

            if (D3VectorNorm(coordPrev-coord) < 1e-25)
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            {
                iter = 1000;
            }
            if (std::isnan(coord.x) || std::isnan(coord.y) || std::isnan(coord.z))
            {
                std::cout << "trilinear interpolation failed!!!\n"<< std::endl;
            }

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            x = A    + B * coord.x + C * coord.y + D * coord.z + E * coord.x*coord.y + F * coord.y*coord.z + G * coord.x * coord.z + H * coord.x*coord.y*coord.z;
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            if (coord.x > 2.0)
                coord.x = 1.1;
            if (coord.y > 2.0)
                coord.y = 1.1;
            if (coord.z > 2.0)
                coord.z = 1.1;
            if (coord.x < -1.0)
                coord.x = -0.1;
            if (coord.y < -1.0)
                coord.y = -0.1;
            if (coord.z < -1.0)
                coord.z = -0.1;

        }



//    X.Print();
//    std::cout << "tirlinear interp \n";
//   x.Print();
//    std::cout << std::flush;


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    if (MAX(coord) > 1.2 || MIN(coord) < -0.2)
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    {
        return D3vector{-1,-1,-1};
    }
    return coord;
}
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Interpolate_on_structured_grid::Interpolate_on_structured_grid(int nx_, int ny_, int nz_,
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                                   D3vector pWSD, D3vector pENT,
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                                   Blockgrid& blockgrid_, bool trilinearInterpolationFlag_) {
   // id = trilinearInterpolationFlag_;
    trilinearInterpolationFlag = trilinearInterpolationFlag_;
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  int Nx, Ny, Nz;
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   int typ;
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  assert(nx_ > 1);
  assert(ny_ > 1);
  assert(nz_ > 1);

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  //int ilmin, jlmin, klmin;
  //int ilmax, jlmax, klmax;
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  double factor = 0.1;
  //  double factor = 0.00001;

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   D3vector lam;
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  blockgrid = &blockgrid_;
  ug = blockgrid->Give_unstructured_grid();

  nx = nx_;
  ny = ny_;
  nz = nz_;

  if(nx_>1)
    hx = (pENT.x - pWSD.x) / (nx_-1);
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  else
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    hx = 1.0;
  if(ny_>1)
    hy = (pENT.y - pWSD.y) / (ny_-1);
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  else
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    hy = 1.0;
  if(nz_>1)
    hz = (pENT.z - pWSD.z) / (nz_-1);
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  else
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    hz = 1.0;

  int num_total = nx * ny * nz;

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  /*
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  D3vector cWSD, cESD;
  D3vector cWND, cEND;

  D3vector cWST, cEST;
  D3vector cWNT, cENT;
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*/
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  // D3vector boxWSD, boxENT;
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  // D3vector ploc;
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  ids_hex = new int[num_total];

  ids_i = new int[num_total];
  ids_j = new int[num_total];
  ids_k = new int[num_total];

  typ_tet = new int[num_total];

  lambda = new D3vector[num_total];

  for(int i=0;i<num_total;++i) ids_hex[i] = -1;

  for(int id_hex=0;id_hex<ug->Give_number_hexahedra();++id_hex) {
      Nx = blockgrid->Give_Nx_hexahedron(id_hex);
      Ny = blockgrid->Give_Ny_hexahedron(id_hex);
      Nz = blockgrid->Give_Nz_hexahedron(id_hex);

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#pragma omp parallel for num_threads(UGBlocks::numThreadsToTake) if(UGBlocks::useOpenMP)
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      for(int k=0;k<Nz;++k)
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    for(int j=0;j<Ny;++j)
      for(int i=0;i<Nx;++i) {
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            // corner points of general hex-cell
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        D3vector cWSD = blockgrid->Give_coord_hexahedron(id_hex,i,  j,  k  );
        D3vector cESD = blockgrid->Give_coord_hexahedron(id_hex,i+1,j  ,k  );
        D3vector cWND = blockgrid->Give_coord_hexahedron(id_hex,i,  j+1,k  );
        D3vector cEND = blockgrid->Give_coord_hexahedron(id_hex,i+1,j+1,k  );

        D3vector cWST = blockgrid->Give_coord_hexahedron(id_hex,i,  j,  k+1);
        D3vector cEST = blockgrid->Give_coord_hexahedron(id_hex,i+1,j  ,k+1);
        D3vector cWNT = blockgrid->Give_coord_hexahedron(id_hex,i,  j+1,k+1);
        D3vector cENT = blockgrid->Give_coord_hexahedron(id_hex,i+1,j+1,k+1);

            // bounding box calculation
        D3vector boxWSD, boxENT;
        boxWSD.x = MIN(MIN(MIN(cWSD.x,cESD.x),MIN(cWND.x,cEND.x)),
               MIN(MIN(cWST.x,cEST.x),MIN(cWNT.x,cENT.x))) - factor *hx;
        boxWSD.y = MIN(MIN(MIN(cWSD.y,cESD.y),MIN(cWND.y,cEND.y)),
               MIN(MIN(cWST.y,cEST.y),MIN(cWNT.y,cENT.y))) - factor *hy;
        boxWSD.z = MIN(MIN(MIN(cWSD.z,cESD.z),MIN(cWND.z,cEND.z)),
               MIN(MIN(cWST.z,cEST.z),MIN(cWNT.z,cENT.z))) - factor *hz;

        boxENT.x = MAX(MAX(MAX(cWSD.x,cESD.x),MAX(cWND.x,cEND.x)),
               MAX(MAX(cWST.x,cEST.x),MAX(cWNT.x,cENT.x))) + factor *hx;
        boxENT.y = MAX(MAX(MAX(cWSD.y,cESD.y),MAX(cWND.y,cEND.y)),
               MAX(MAX(cWST.y,cEST.y),MAX(cWNT.y,cENT.y))) + factor *hy;
        boxENT.z = MAX(MAX(MAX(cWSD.z,cESD.z),MAX(cWND.z,cEND.z)),
               MAX(MAX(cWST.z,cEST.z),MAX(cWNT.z,cENT.z))) + factor *hz;

        // calculation of indices of a collection of cells of structured grid which contains bounding box
        int ilmin = Ganzzahliger_Anteil((boxWSD.x - pWSD.x) / hx);
        int jlmin = Ganzzahliger_Anteil((boxWSD.y - pWSD.y) / hy);
        int klmin = Ganzzahliger_Anteil((boxWSD.z - pWSD.z) / hz);


        int ilmax = Ganzzahliger_Anteil((boxENT.x - pWSD.x) / hx);
        int jlmax = Ganzzahliger_Anteil((boxENT.y - pWSD.y) / hy);
        int klmax = Ganzzahliger_Anteil((boxENT.z - pWSD.z) / hz);

        /*
        cout << " indices: "
         << " ilmin: " << ilmin
         << " jlmin: " << jlmin
         << " klmin: " << klmin
         << " ilmax: " << ilmax
         << " jlmax: " << jlmax
         << " klmax: " << klmax
         << " boxWSD.x: " << boxWSD.x
         << " cWSD.x: " << cWSD.x
         << " Nx: " <<  Nx
         << endl;
        */
        /*
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bool now;
if(boxWSD.z < 0 && boxENT.z > 0.0 && boxWSD.y < 0.5 && boxENT.y > 0.5 && boxWSD.x < 1.0 && boxENT.x > 1.0 ) {
  cout << "\n \n WSD   : ";  boxWSD.Print();
  cout << "\n ENT  : ";  boxENT.Print();
  now = true;
 }
 else now = false;

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 cout << " tt: " << boxWSD.x << " " << pWSD.x << " " << hx << endl;
 cout << (boxWSD.x - pWSD.x) << endl;

 cout << " z: " << 0.1 << " g: " << Ganzzahliger_Anteil(0.1) << endl;
 cout << " z: " << -0.1 << " g: " << Ganzzahliger_Anteil(-0.1) << endl;

 cout << " z: " << 5.1 << " g: " << Ganzzahliger_Anteil(5.1) << endl;
 cout << " z: " << -5.1 << " g: " << Ganzzahliger_Anteil(-5.1) << endl;
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        */

        if(ilmin<0) ilmin=0;
        if(jlmin<0) jlmin=0;
        if(klmin<0) klmin=0;

        for(int il = ilmin; (il <= ilmax) && (il < nx_);++il)
          for(int jl = jlmin; (jl <= jlmax) && (jl < ny_);++jl)
        for(int kl = klmin; (kl <= klmax) && (kl < nz_);++kl) {

          D3vector ploc = D3vector(il * hx, jl * hy, kl * hz) + pWSD;

          //		  cout << "HI" << endl;


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          typ = -1;

          lam = lambda_of_p_in_tet(ploc,cWND,cWNT,cWST,cEST);
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          if(contained_in_tet(lam)) typ=0;
          else {
            lam = lambda_of_p_in_tet(ploc,cEST,cWND,cWST,cESD);
            if(contained_in_tet(lam)) typ=1;
            else {
              lam = lambda_of_p_in_tet(ploc,cWND,cWSD,cWST,cESD);
              if(contained_in_tet(lam)) typ=2;
              else {
            lam = lambda_of_p_in_tet(ploc,cEST,cWND,cESD,cEND);
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            if(contained_in_tet(lam))
            {typ=3;lambda_of_p_in_tet(ploc,cEST,cWND,cESD,cEND);}
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            else {
              lam = lambda_of_p_in_tet(ploc,cENT,cWNT,cEST,cEND);
              if(contained_in_tet(lam)) typ=4;
              else {
                lam = lambda_of_p_in_tet(ploc,cWNT,cWND,cEST,cEND);
                if(contained_in_tet(lam)) typ=5;
              }
            }
              }
            }
          }
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          if (trilinearInterpolationFlag && MIN(lam)>= -0.1 && MAX(lam) <= 1.1 && SUM(lam) <= 1.2 && SUM(lam)>=-0.2)
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          {
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              lam = trilinarInterpolation(ploc, id_hex,i,  j,  k);
              typ = 6;
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          }
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          /*
          cout << " typ " << typ << id_hex
               << " il: " << il
               << " jl: " << jl
               << " kl: " << kl
               << endl;
          */

          if(typ!=-1) {
            int ind_global;
            ind_global = il+nx*(jl+ny*kl);
            bool stop;
            stop=false;

            if(ids_hex[ind_global]!=-1) {
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              stop=new_lam_worse(lambda[ind_global],lam);
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            }

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            if(stop==false) {
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              ids_hex[ind_global] = id_hex;
              ids_i[ind_global] = i;
              ids_j[ind_global] = j;
              ids_k[ind_global] = k;

              typ_tet[ind_global] = typ;

              lambda[ind_global] = lam;
            }
            //go_on = false;
          }

          /*
          cout << " out "
               << " ilmin: " << ilmin
               << " ilmax: " << ilmax
               << " jlmin: " << jlmin
               << " jlmax: " << jlmax
               << " klmin: " << klmin
               << " klmax: " << klmax;
          cout << "\n   "; cWSD.Print();
          cout << "\n   "; cESD.Print();
          cout << "\n   "; cWND.Print();
          cout << "\n   "; cEND.Print();
          cout << "\n   "; cWST.Print();
          cout << "\n   "; cEST.Print();
          cout << "\n   "; cWNT.Print();
          cout << "\n   "; cENT.Print();
          cout << "\n   p: "; ploc.Print();

          cout << "\n   : ";  boxWSD.Print();
          cout << "\n   : ";  boxENT.Print();

          cout << endl;
          */
        }
      }
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  }


  for(int i=0;i<num_total;++i) {
    if(ids_hex[i]==-1) {
      // wir nehmen default value!!
      /*
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      cout << i
       << " Error: Interpolate_on_structured_grid: I cannot interpolate all data!"
       << endl;
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      ids_hex[i] = 0;
      */
    }
    else {
      //cout << i << " Interpolate_on_structured_grid: o.k.!" << endl;
    }
  }
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//  for ( int iter = 0 ; iter < num_total ; iter++)
//  {
//      std::cout << "typtet " << typ_tet[iter] <<"\n";
//  }
//  std::cout << std::endl;
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}

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/////////////////////////////////////////////////////////////
// 2. Interpolate from  blockgrid  to  blockgrid
/////////////////////////////////////////////////////////////


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Interpolate_on_structured_grid::Interpolate_on_structured_grid(int nx_, int ny_, int nz_,
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                                   Blockgrid& blockgrid_, bool trilinearInterpolationFlag_) {
    //id = trilinearInterpolationFlag_;
    trilinearInterpolationFlag = trilinearInterpolationFlag_;
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  int Nx, Ny, Nz;
  int typ;

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  assert(nx_ > 1);
  assert(ny_ > 1);
  assert(nz_ > 1);

  int ilmin, jlmin, klmin;
  int ilmax, jlmax, klmax;

  double factor = 0.1;
  //  double factor = 0.00001;

  D3vector lam;

     
    
    //Variable<double> coordXYZ(*blockgrid);
    X_coordinate Xc(blockgrid_);
    Y_coordinate Yc(blockgrid_);
    Z_coordinate Zc(blockgrid_);
    //D3vector pWSD, pENT;
    pWSD.x = Minimum(Xc);    pWSD.y = Minimum(Yc);    pWSD.z = Minimum(Zc);
    pENT.x = Maximum(Xc);    pENT.y = Maximum(Yc);    pENT.z = Maximum(Zc);  
  
  blockgrid = &blockgrid_;
  ug = blockgrid->Give_unstructured_grid();

  nx = nx_;
  ny = ny_;
  nz = nz_;

  if(nx_>1)
    hx = (pENT.x - pWSD.x) / (nx_-1);
  else  
    hx = 1.0;
  if(ny_>1)
    hy = (pENT.y - pWSD.y) / (ny_-1);
  else  
    hy = 1.0;
  if(nz_>1)
    hz = (pENT.z - pWSD.z) / (nz_-1);
  else 
    hz = 1.0;
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  int num_total = nx * ny * nz;

  D3vector cWSD, cESD;
  D3vector cWND, cEND;

  D3vector cWST, cEST;
  D3vector cWNT, cENT;

  D3vector boxWSD, boxENT;

  D3vector ploc;
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  ids_hex = new int[num_total];

  ids_i = new int[num_total];
  ids_j = new int[num_total];
  ids_k = new int[num_total];

  typ_tet = new int[num_total];

  lambda = new D3vector[num_total];

  for(int i=0;i<num_total;++i) ids_hex[i] = -1;

  for(int id_hex=0;id_hex<ug->Give_number_hexahedra();++id_hex) {
      Nx = blockgrid->Give_Nx_hexahedron(id_hex);
      Ny = blockgrid->Give_Ny_hexahedron(id_hex);
      Nz = blockgrid->Give_Nz_hexahedron(id_hex);
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      for(int k=0;k<Nz;++k)
	for(int j=0;j<Ny;++j)
	  for(int i=0;i<Nx;++i) {
            // corner points of general hex-cell
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	    cWSD = blockgrid->Give_coord_hexahedron(id_hex,i,  j,  k  );
	    cESD = blockgrid->Give_coord_hexahedron(id_hex,i+1,j  ,k  );
	    cWND = blockgrid->Give_coord_hexahedron(id_hex,i,  j+1,k  );
	    cEND = blockgrid->Give_coord_hexahedron(id_hex,i+1,j+1,k  );
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	    cWST = blockgrid->Give_coord_hexahedron(id_hex,i,  j,  k+1);
	    cEST = blockgrid->Give_coord_hexahedron(id_hex,i+1,j  ,k+1);
	    cWNT = blockgrid->Give_coord_hexahedron(id_hex,i,  j+1,k+1);
	    cENT = blockgrid->Give_coord_hexahedron(id_hex,i+1,j+1,k+1);
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            // bounding box calculation 
	    boxWSD.x = MIN(MIN(MIN(cWSD.x,cESD.x),MIN(cWND.x,cEND.x)),
			   MIN(MIN(cWST.x,cEST.x),MIN(cWNT.x,cENT.x))) - factor *hx;
	    boxWSD.y = MIN(MIN(MIN(cWSD.y,cESD.y),MIN(cWND.y,cEND.y)),
			   MIN(MIN(cWST.y,cEST.y),MIN(cWNT.y,cENT.y))) - factor *hy;
	    boxWSD.z = MIN(MIN(MIN(cWSD.z,cESD.z),MIN(cWND.z,cEND.z)),
			   MIN(MIN(cWST.z,cEST.z),MIN(cWNT.z,cENT.z))) - factor *hz;

	    boxENT.x = MAX(MAX(MAX(cWSD.x,cESD.x),MAX(cWND.x,cEND.x)),
			   MAX(MAX(cWST.x,cEST.x),MAX(cWNT.x,cENT.x))) + factor *hx;
	    boxENT.y = MAX(MAX(MAX(cWSD.y,cESD.y),MAX(cWND.y,cEND.y)),
			   MAX(MAX(cWST.y,cEST.y),MAX(cWNT.y,cENT.y))) + factor *hy;
	    boxENT.z = MAX(MAX(MAX(cWSD.z,cESD.z),MAX(cWND.z,cEND.z)),
			   MAX(MAX(cWST.z,cEST.z),MAX(cWNT.z,cENT.z))) + factor *hz;

	    // calculation of indices of a collection of cells of structured grid which contains bounding box
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	    ilmin = Ganzzahliger_Anteil((boxWSD.x - pWSD.x) / hx);
	    jlmin = Ganzzahliger_Anteil((boxWSD.y - pWSD.y) / hy);
	    klmin = Ganzzahliger_Anteil((boxWSD.z - pWSD.z) / hz);
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	    ilmax = Ganzzahliger_Anteil((boxENT.x - pWSD.x) / hx);
	    jlmax = Ganzzahliger_Anteil((boxENT.y - pWSD.y) / hy);
	    klmax = Ganzzahliger_Anteil((boxENT.z - pWSD.z) / hz);
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	    /*
	    cout << " indices: "
		 << " ilmin: " << ilmin 
		 << " jlmin: " << jlmin 
		 << " klmin: " << klmin 
		 << " ilmax: " << ilmax 
		 << " jlmax: " << jlmax 
		 << " klmax: " << klmax 
		 << " boxWSD.x: " << boxWSD.x
		 << " cWSD.x: " << cWSD.x
		 << " Nx: " <<  Nx
		 << endl;
	    */
	    /*	    
bool now;
if(boxWSD.z < 0 && boxENT.z > 0.0 && boxWSD.y < 0.5 && boxENT.y > 0.5 && boxWSD.x < 1.0 && boxENT.x > 1.0 ) {
  cout << "\n \n WSD   : ";  boxWSD.Print();
  cout << "\n ENT  : ";  boxENT.Print();
  now = true;
 }
 else now = false;

 
 cout << " tt: " << boxWSD.x << " " << pWSD.x << " " << hx << endl;
 cout << (boxWSD.x - pWSD.x) << endl;

 cout << " z: " << 0.1 << " g: " << Ganzzahliger_Anteil(0.1) << endl;
 cout << " z: " << -0.1 << " g: " << Ganzzahliger_Anteil(-0.1) << endl;

 cout << " z: " << 5.1 << " g: " << Ganzzahliger_Anteil(5.1) << endl;
 cout << " z: " << -5.1 << " g: " << Ganzzahliger_Anteil(-5.1) << endl;
	    */

	    if(ilmin<0) ilmin=0;
	    if(jlmin<0) jlmin=0;
	    if(klmin<0) klmin=0;

	    for(int il = ilmin; (il <= ilmax) && (il < nx_);++il)
	      for(int jl = jlmin; (jl <= jlmax) && (jl < ny_);++jl)
		for(int kl = klmin; (kl <= klmax) && (kl < nz_);++kl) {

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		  ploc = D3vector(il * hx, jl * hy, kl * hz) + pWSD;
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		  //		  cout << "HI" << endl;

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		  typ = -1;
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		  lam = lambda_of_p_in_tet(ploc,cWND,cWNT,cWST,cEST);
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		  if(contained_in_tet(lam)) typ=0;
		  else {
		    lam = lambda_of_p_in_tet(ploc,cEST,cWND,cWST,cESD);
		    if(contained_in_tet(lam)) typ=1;
		    else {
		      lam = lambda_of_p_in_tet(ploc,cWND,cWSD,cWST,cESD);
		      if(contained_in_tet(lam)) typ=2;
		      else {
			lam = lambda_of_p_in_tet(ploc,cEST,cWND,cESD,cEND);
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            if(contained_in_tet(lam))
            {typ=3;lambda_of_p_in_tet(ploc,cEST,cWND,cESD,cEND);}
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			else {
			  lam = lambda_of_p_in_tet(ploc,cENT,cWNT,cEST,cEND);
			  if(contained_in_tet(lam)) typ=4;
			  else {
			    lam = lambda_of_p_in_tet(ploc,cWNT,cWND,cEST,cEND);
			    if(contained_in_tet(lam)) typ=5;
			  }
			}
		      }
		    }
		  }
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          if (trilinearInterpolationFlag && MIN(lam)>= -0.2 && MAX(lam) <= 1.2 && SUM(lam) <= 1.2 && SUM(lam)>=-0.2)
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          {
              lam = trilinarInterpolation(ploc, id_hex,i,  j,  k);
              typ = 6;
          }
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		  /*		  
		  cout << " typ " << typ << id_hex 
		       << " il: " << il 
		       << " jl: " << jl 
		       << " kl: " << kl 
		       << endl; 
		  */

		  if(typ!=-1) {
		    int ind_global;
		    ind_global = il+nx*(jl+ny*kl);      
		    bool stop;
		    stop=false;

		    if(ids_hex[ind_global]!=-1) {
		      stop=new_lam_worse(lambda[ind_global],lam);
		    }

		    if(stop==false) {
		      ids_hex[ind_global] = id_hex;
		      ids_i[ind_global] = i;
		      ids_j[ind_global] = j;
		      ids_k[ind_global] = k;
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		      typ_tet[ind_global] = typ;
		      
		      lambda[ind_global] = lam;
		    }
		    //go_on = false;
		  }

		  /*
		  cout << " out "
		       << " ilmin: " << ilmin
		       << " ilmax: " << ilmax
		       << " jlmin: " << jlmin
		       << " jlmax: " << jlmax
		       << " klmin: " << klmin
		       << " klmax: " << klmax;
		  cout << "\n   "; cWSD.Print();
		  cout << "\n   "; cESD.Print();
		  cout << "\n   "; cWND.Print();
		  cout << "\n   "; cEND.Print();
		  cout << "\n   "; cWST.Print();
		  cout << "\n   "; cEST.Print();
		  cout << "\n   "; cWNT.Print();
		  cout << "\n   "; cENT.Print();
		  cout << "\n   p: "; ploc.Print();

		  cout << "\n   : ";  boxWSD.Print();
		  cout << "\n   : ";  boxENT.Print();

		  cout << endl;
		  */
		}
	  }
  }


  for(int i=0;i<num_total;++i) {
    if(ids_hex[i]==-1) {
      // wir nehmen default value!!
      /*
      cout << i 
	   << " Error: Interpolate_on_structured_grid: I cannot interpolate all data!"
	   << endl;
      ids_hex[i] = 0;
      */
    }
    else {
      //cout << i << " Interpolate_on_structured_grid: o.k.!" << endl;
    }
  }
}

/////////////////////////////////////////////////////////////
// 2. Interpolate from  blockgrid  to  blockgrid
/////////////////////////////////////////////////////////////


Interpolate_on_block_grid::Interpolate_on_block_grid(int nx_, int ny_, int nz_,
				                     Blockgrid* blockgrid_from, Blockgrid* blockgrid_to_) {
    nx = nx_;
    ny = ny_;
    nz = nz_;
 
    if(nx<=2) nx = 3;
    if(ny<=2) ny = 3;
    if(nz<=2) nz = 3;
     
    blockgrid_to = blockgrid_to_;
    
    //Variable<double> coordXYZ(*blockgrid);
    X_coordinate Xc(*blockgrid_to);
    Y_coordinate Yc(*blockgrid_to);
    Z_coordinate Zc(*blockgrid_to);
    
    pWSD.x = Minimum(Xc);    pWSD.y = Minimum(Yc);    pWSD.z = Minimum(Zc);
    pENT.x = Maximum(Xc);    pENT.y = Maximum(Yc);    pENT.z = Maximum(Zc);  

    interpolatorStructured = new Interpolate_on_structured_grid(nx,ny,nz, pWSD, pENT, *blockgrid_from);
    data = new double[nx*ny*nz];
    
    
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    hx = (pENT.x - pWSD.x) / (nx-1);
    hy = (pENT.y - pWSD.y) / (ny-1);
    hz = (pENT.z - pWSD.z) / (nz-1);
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    /*
    
    // test GGGG
    cout << "\n WSD: " ; pWSD.Print();
    cout << "\n ENT: " ; pENT.Print();
    cout << "nx: " << nx << " ny: " << ny << " nz: " << nz << endl;
    */
}
  

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void Interpolate_on_block_grid::interpolate(Variable<double>* U_from, Variable<double>* U_to,
					    double defaultInterpolation) {
/*
   //test GGGG
   X_coordinate Xfrom(*U_from->Give_blockgrid());
  (*U_from) = Xfrom;  
*/  
    interpolatorStructured->interpolate<double>(*U_from,data,defaultInterpolation);

    /*
 //test GGGG
    for(int i=0;i<Nx;++i) for(int j=0;j<nz;++j) for(int k=0;k<nz;++k) 
       data[i    +nx*(j    +ny* k)] = hx * i;
      */
      
    Functor3<double,double,Interpolate_on_block_grid> myFunctor(this);
    
    X_coordinate Xc(*blockgrid_to);
    Y_coordinate Yc(*blockgrid_to);
    Z_coordinate Zc(*blockgrid_to);
    
    (*U_to) = myFunctor(Xc,Yc,Zc);
}
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double Interpolate_on_block_grid::evaluate(double coord_x, double coord_y, double coord_z) {  
  if(coord_x > pENT.x) return 0.0;
  if(coord_x < pWSD.x) return 0.0;
  if(coord_y > pENT.y) return 0.0;
  if(coord_y < pWSD.y) return 0.0;
  if(coord_z > pENT.z) return 0.0;
  if(coord_z < pWSD.z) return 0.0;
  
  int i = (coord_x - pWSD.x) / hx;   
  int j = (coord_y - pWSD.y) / hy;   
  int k = (coord_z - pWSD.z) / hz;   
    
  if(i < 0)   i=0;     if(j <0   ) j=0;     if(k<0)     k=0;
  if(i>=nx-1) i=nx-2;  if(j>=ny-1) j=ny-2;  if(k>=nz-1) k=nz-2;
  
  //cout << "i: " << i << " j: " << j << " k: " << k << endl;
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  double uWSD = data[i    +nx*(j    +ny* k)];
  double uESD = data[(i+1)+nx*(j    +ny* k)];
  double uWND = data[i    +nx*((j+1)+ny* k)];
  double uEND = data[(i+1)+nx*((j+1)+ny* k)];
  double uWST = data[i    +nx*(j    +ny*(k+1))];
  double uEST = data[(i+1)+nx*(j    +ny*(k+1))];
  double uWNT = data[i    +nx*((j+1)+ny*(k+1))];
  double uENT = data[(i+1)+nx*((j+1)+ny*(k+1))];
  
  
  // assert( (i+1)+nx*((j+1)+ny*(k+1)) < nx*ny*nz);
  
  double locX = (coord_x - pWSD.x) / hx - i;
  double locY = (coord_y - pWSD.y) / hy - j;
  double locZ = (coord_z - pWSD.z) / hz - k;
  
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  return uWSD * (1.0 - locX) * (1.0 - locY) * (1.0 - locZ) +
         uESD *        locX  * (1.0 - locY) * (1.0 - locZ) +
         uWND * (1.0 - locX) *        locY  * (1.0 - locZ) +
         uEND *        locX  *        locY  * (1.0 - locZ) +
         uWST * (1.0 - locX) * (1.0 - locY) *        locZ  +
         uEST *        locX  * (1.0 - locY) *        locZ  +
         uWNT * (1.0 - locX) *        locY  *        locZ  +
         uENT *        locX  *        locY  *        locZ;
}
 
Interpolate_on_block_grid::~Interpolate_on_block_grid() {
    delete interpolatorStructured;
    delete[] data;
}


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/////////////////////////////////////////////////////////////
// 3. Interpolate from Variable on a blockgrid to any point using structured intermediate grid  
/////////////////////////////////////////////////////////////
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PointInterpolator::PointInterpolator(int nx_, int ny_, int nz_,
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                     Variable<double>* U_from, double defaultInterpolation_, bool trilinearInterpolation_ ) {
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    defaultInterpolation = defaultInterpolation_;
    shiftx = 0.0;
    shifty = 0.0;
    shiftz = 0.0;
    nx = nx_;
    ny = ny_;
    nz = nz_;
 
    if(nx<=2) nx = 3;
    if(ny<=2) ny = 3;
    if(nz<=2) nz = 3;
     
    Blockgrid* blockgrid_from = U_from->Give_blockgrid();
    
    //Variable<double> coordXYZ(*blockgrid);
    X_coordinate Xc(*blockgrid_from);
    Y_coordinate Yc(*blockgrid_from);
    Z_coordinate Zc(*blockgrid_from);
    pWSD.x = Minimum(Xc);    pWSD.y = Minimum(Yc);    pWSD.z = Minimum(Zc);
    pENT.x = Maximum(Xc);    pENT.y = Maximum(Yc);    pENT.z = Maximum(Zc);  


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    interpolatorStructured = new Interpolate_on_structured_grid(nx,ny,nz, pWSD, pENT, *blockgrid_from, trilinearInterpolation_);
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    data = new double[nx*ny*nz];
    
    
    hx = (pENT.x - pWSD.x) / (nx-1);
    hy = (pENT.y - pWSD.y) / (ny-1);
    hz = (pENT.z - pWSD.z) / (nz-1);

    interpolatorStructured->interpolate<double>(*U_from,data,defaultInterpolation_);

    
    /*
    
    // test GGGG
    cout << "\n WSD: " ; pWSD.Print();
    cout << "\n ENT: " ; pENT.Print();
    cout << "nx: " << nx << " ny: " << ny << " nz: " << nz << endl;
    */
}
  
PointInterpolator::PointInterpolator(int nx_, int ny_, int nz_,
				     D3vector pWSD_, D3vector pENT_,
				     Variable<double>* U_from, double defaultInterpolation_) {
    defaultInterpolation = defaultInterpolation_;
  
    shiftx = 0.0;
    shifty = 0.0;
    shiftz = 0.0;
    nx = nx_;
    ny = ny_;
    nz = nz_;
 
    if(nx<=2) nx = 3;
    if(ny<=2) ny = 3;
    if(nz<=2) nz = 3;
     
    Blockgrid* blockgrid_from = U_from->Give_blockgrid();
        
    pWSD = pWSD_;
    pENT = pENT_; 

    interpolatorStructured = new Interpolate_on_structured_grid(nx,ny,nz, pWSD, pENT, *blockgrid_from);
    data = new double[nx*ny*nz];
    
    
    hx = (pENT.x - pWSD.x) / (nx-1);
    hy = (pENT.y - pWSD.y) / (ny-1);
    hz = (pENT.z - pWSD.z) / (nz-1);
    
    
    interpolatorStructured->interpolate<double>(*U_from,data,defaultInterpolation);
    
   
    
    
    /*
    
    // test GGGG
    cout << "\n WSD: " ; pWSD.Print();
    cout << "\n ENT: " ; pENT.Print();
    cout << "nx: " << nx << " ny: " << ny << " nz: " << nz << endl;
    */
}

PointInterpolator::PointInterpolator(Interpolate_on_structured_grid* intermediateGrid, Variable<double>* U_from, double defaultInterpolation_)
{
    defaultInterpolation = defaultInterpolation_;
  
    nx = intermediateGrid->nx;
    ny = intermediateGrid->ny;
    nz = intermediateGrid->nz;
    
    data = new double[nx*ny*nz];
    
    pENT = intermediateGrid->pENT;
    pWSD = intermediateGrid->pWSD;
    
    shiftx = 0.0;
    shifty = 0.0;
    shiftz = 0.0;
    hx = (pENT.x - pWSD.x) / (nx-1);
    hy = (pENT.y - pWSD.y) / (ny-1);
    hz = (pENT.z - pWSD.z) / (nz-1);

    intermediateGrid->interpolate<double>(*U_from,data,defaultInterpolation_);
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}

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PointInterpolator::PointInterpolator(Interpolate_on_structured_grid *intermediateGrid, double defaultInterpolation_, bool counter)
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{
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    dataCounterFlag = counter;
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    defaultInterpolation = defaultInterpolation_;

    nx = intermediateGrid->nx;
    ny = intermediateGrid->ny;
    nz = intermediateGrid->nz;

    data = new double[nx*ny*nz];
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    if (counter)
    {
        dataCounter = new int[nx*ny*nz];
    }
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    for (int iter = 0 ; iter < nx*ny*nz;iter++)
    {
        data[iter]=0.0;
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        if (counter)
        {
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        dataCounter[iter]=0;
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        }
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    }

    pENT = intermediateGrid->pENT;
    pWSD = intermediateGrid->pWSD;

    hx = intermediateGrid->getHx();
    hy = intermediateGrid->getHy();
    hz = intermediateGrid->getHz();

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    interpolatorStructured = intermediateGrid;

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}
 
 /*
Interpolate_on_structured_grid* PointInterpolator::intermediateGrid(int nx_, int ny_, int nz_, Variable<double>* U_from)
{
    nx = nx_;
    ny = ny_;
    nz = nz_;
 
    if(nx<=2) nx = 3;
    if(ny<=2) ny = 3;
    if(nz<=2) nz = 3;
     
    Blockgrid* blockgrid_from = U_from->Give_blockgrid();
    
    //Variable<double> coordXYZ(*blockgrid);
    X_coordinate Xc(*blockgrid_from);
    Y_coordinate Yc(*blockgrid_from);
    Z_coordinate Zc(*blockgrid_from);
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    pWSD.x = Minimum(Xc);    pWSD.y = Minimum(Yc);    pWSD.z = Minimum(Zc);
    pENT.x = Maximum(Xc);    pENT.y = Maximum(Yc);    pENT.z = Maximum(Zc);  
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    interpolatorStructured = new Interpolate_on_structured_grid(nx,ny,nz, pWSD, pENT, *blockgrid_from);
    
    return interpolatorStructured;
}
*/


 
double PointInterpolator::evaluate(double coord_x, double coord_y, double coord_z) {  

    coord_x-=shiftx;
    coord_y-=shifty;
    coord_z-=shiftz;

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  if(coord_x > (pENT.x+(1e-9))) return defaultInterpolation;
  if(coord_x < (pWSD.x-(1e-9))) return defaultInterpolation;
  if(coord_y > (pENT.y+(1e-9))) return defaultInterpolation;
  if(coord_y < (pWSD.y-(1e-9))) return defaultInterpolation;
  if(coord_z > (pENT.z+(1e-9))) return defaultInterpolation;
  if(coord_z < (pWSD.z-(1e-9))) return defaultInterpolation;
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  //cout << "coord_z " << coord_z << " pWSD.z " << pWSD.z << endl;
    /*
  int i = (coord_x - pWSD.x) / hx;
  int j = (coord_y - pWSD.y) / hy;
  int k = (coord_z - pWSD.z) / hz;
  */
  double id = (coord_x - pWSD.x) / hx;
  double jd = (coord_y - pWSD.y) / hy;
  double kd = (coord_z - pWSD.z) / hz;


  int i = int(id);
  int j = int(jd);
  int k = int(kd);

  if(i < 0)   i=0;     if(j <0   ) j=0;     if(k<0)     k=0;
  if(i>=nx-1) i=nx-2;  if(j>=ny-1) j=ny-2;  if(k>=nz-1) k=nz-2;



  //cout << "hx " << hx << " hy "<< hy << " hz " << hz << endl;
  //cout << "id: " << id << " jd: " << jd << " kd: " << kd << endl;
  //cout << "i: " << i << " j: " << j << " k: " << k << endl;
  //cout << "nx: " << nx << " ny: " << ny << " nz: " << nz << endl;


  double uWSD = data[i    +nx*(j    +ny* k)];
  double uESD = data[(i+1)+nx*(j    +ny* k)];
  double uWND = data[i    +nx*((j+1)+ny* k)];
  double uEND = data[(i+1)+nx*((j+1)+ny* k)];
  double uWST = data[i    +nx*(j    +ny*(k+1))];
  double uEST = data[(i+1)+nx*(j    +ny*(k+1))];
  double uWNT = data[i    +nx*((j+1)+ny*(k+1))];
  double uENT = data[(i+1)+nx*((j+1)+ny*(k+1))];
  //i++;
  //j++;
  //k++;
  //k++;
  //cout << "uWSD " << uWSD << endl;
  //cout << "uESD " << uESD << endl;
  //cout << "uWND " << uWND << endl;
  //cout << "uEND " << uEND << endl;
  //cout << "uWST " << uWST << endl;
  //cout << "uEST " << uEST << endl;
  //cout << "uWNT " << uWNT << endl;
  //cout << "uENT " << uENT << endl;


  //cout << "x+1 "<< data[(i+2)+nx*(j    +ny* k)] << endl;
  //cout << "x-1 " <<data[i-1    +nx*(j    +ny* k)] << endl;
  //cout << "x-1, y-1 " <<data[i-1    +nx*(j-1    +ny* k)] << endl;

  // assert( (i+1)+nx*((j+1)+ny*(k+1)) < nx*ny*nz);
  
  double posX = (coord_x - pWSD.x) ;
  double locX = posX / hx - i;
  double posY = (coord_y - pWSD.y);
  double locY = posY / hy - j;
  double posZ = (coord_z - pWSD.z);
  double locZ = posZ / hz - k;



  //cout << "locX, Y, Z: " << locX << " " << locY << " " << locZ << endl;
  //return uWSD;
  
  
  //cout << "uPOS : " << uWSD << " , " << uESD << " , " << uWND << " , " << uEND << " , " << uWST << " , " << uEST << " , " << uWNT << " , " << uENT << endl;
  double uTOT(0);
  double uET, uWT, uWD, uED;
  double uT, uD;

  if      ( (uEST != defaultInterpolation) == (uENT != defaultInterpolation) ) { uET = uEST * (1.0 - locY) + uENT * locY ;}
  else if ( (uEST != defaultInterpolation) && (uENT == defaultInterpolation) ) { uET = uEST;}
  else     								       { uET = uENT;}
  
  if      ( (uWST != defaultInterpolation) == (uWNT != defaultInterpolation) ) {uWT = uWST * (1.0 - locY) + uWNT * locY ;}
  else if ( (uWST != defaultInterpolation) && (uWNT == defaultInterpolation) ) {uWT = uWST;}
  else     								       {uWT = uWNT;}
  
  if      ( (uESD != defaultInterpolation) == (uEND != defaultInterpolation) ) {uED = uESD * (1.0 - locY) + uEND * locY ;}
  else if ( (uESD != defaultInterpolation) && (uEND == defaultInterpolation) ) {uED = uESD;}
  else  								       {uED = uEND;}
  
  if      ( (uWSD != defaultInterpolation) == (uWND != defaultInterpolation) ) {uWD = uWSD * (1.0 - locY) + uWND * locY ;}
  else if ( (uWSD != defaultInterpolation) && (uWND == defaultInterpolation) ) {uWD = uWSD;}
  else     								       {uWD = uWND;}
    
  if      ( (uET != defaultInterpolation)  == (uWT != defaultInterpolation)  ) {uT = uWT  * (1.0 - locX) + uET  * locX ;}
  else if ( (uET != defaultInterpolation)  && (uWT == defaultInterpolation)  ) {uT = uET;}
  else     								       {uT = uWT;}
  
  if      ( (uED != defaultInterpolation)  == (uWD != defaultInterpolation)  ) {uD = uWD  * (1.0 - locX) + uED  * locX ;}
  else if ( (uED != defaultInterpolation)  && (uWD == defaultInterpolation)  ) {uD = uED;}
  else     								       {uD = uWD;}
  
  if      ( (uT != defaultInterpolation)   == (uD != defaultInterpolation)   ) {uTOT = uD   * (1.0 - locZ) + uT   * locZ ;}
  else if ( (uT != defaultInterpolation)   && (uD == defaultInterpolation)   ) {uTOT = uT;}
  else    								       {uTOT = uD;}



//  if (uWSD != defaultInterpolation)
//  {    uTOT += uWSD * (1.0 - locX) * (1.0 - locY) * (1.0 - locZ);  }
//  if (uESD != defaultInterpolation)
//  {    uTOT += uESD *        locX  * (1.0 - locY) * (1.0 - locZ);  }
//  if (uWND != defaultInterpolation)
//  {    uTOT += uWND * (1.0 - locX) *        locY  * (1.0 - locZ);  }
//  if (uEND != defaultInterpolation)
//  {    uTOT += uEND *        locX  *        locY  * (1.0 - locZ);  }
//  if (uWST != defaultInterpolation)
//  {    uTOT += uWST * (1.0 - locX) * (1.0 - locY) *        locZ;  }
//  if (uEST != defaultInterpolation)
//  {    uTOT += uEST *        locX  * (1.0 - locY) *        locZ;  }
//  if (uWNT != defaultInterpolation)
//  {    uTOT += uWNT * (1.0 - locX) *        locY  *        locZ;  }
//  if (uENT != defaultInterpolation)
//  {    uTOT += uENT *        locX  *        locY  *        locZ;  }

    //cout << "my method, other method " << uTOT << " , " << uWSD * (1.0 - locX) * (1.0 - locY) * (1.0 - locZ) +
    //     uESD *        locX  * (1.0 - locY) * (1.0 - locZ) +
   //      uWND * (1.0 - locX) *        locY  * (1.0 - locZ) +
    //     uEND *        locX  *        locY  * (1.0 - locZ) +
   //      uWST * (1.0 - locX) * (1.0 - locY) *        locZ  +
   //      uEST *        locX  * (1.0 - locY) *        locZ  +
    //     uWNT * (1.0 - locX) *        locY  *        locZ  +
    //     uENT *        locX  *        locY  *        locZ << endl;


  //cout <<endl<< "RESULT: " << uTOT<<endl<<endl;
  return uTOT;


  

  /*
  return uWSD * (1.0 - locX) * (1.0 - locY) * (1.0 - locZ) +
         uESD *        locX  * (1.0 - locY) * (1.0 - locZ) +
         uWND * (1.0 - locX) *        locY  * (1.0 - locZ) +
         uEND *        locX  *        locY  * (1.0 - locZ) +
         uWST * (1.0 - locX) * (1.0 - locY) *        locZ  +
         uEST *        locX  * (1.0 - locY) *        locZ  +
         uWNT * (1.0 - locX) *        locY  *        locZ  +
         uENT *        locX  *        locY  *        locZ;
  */
}

std::vector<double> PointInterpolator::evaluateGradient(double coord_x, double coord_y, double coord_z){
    coord_x-=shiftx;
    coord_y-=shifty;
    coord_z-=shiftz;
    //cout << "coord_x y z " << coord_x << " " << coord_y << " " << coord_z << endl;
    if(coord_x > pENT.x) return std::vector<double>({0.0 , 0.0 , 0.0});
    if(coord_x < pWSD.x) return std::vector<double>({0.0 , 0.0 , 0.0});
    if(coord_y > pENT.y) return std::vector<double>({0.0 , 0.0 , 0.0});
    if(coord_y < pWSD.y) return std::vector<double>({0.0 , 0.0 , 0.0});
    if(coord_z > pENT.z) return std::vector<double>({0.0 , 0.0 , 0.0});
    if(coord_z < pWSD.z) return std::vector<double>({0.0 , 0.0 , 0.0});


    double id = (coord_x - pWSD.x) / hx;
    double jd = (coord_y - pWSD.y) / hy;
    double kd = (coord_z - pWSD.z) / hz;


    int i = int(id);
    int j = int(jd);
    int k = int(kd);

    if(i < 0)   i=0;     if(j <0   ) j=0;     if(k<0)     k=0;
    if(i>=nx-1) i=nx-2;  if(j>=ny-1) j=ny-2;  if(k>=nz-1) k=nz-2;


    //cout << "coord_i j k " << i << " " << j << " " << k << endl;





    double uWSD = data[i    +nx*(j    +ny* k)];
    double uESD = data[(i+1)+nx*(j    +ny* k)];
    double uWND = data[i    +nx*((j+1)+ny* k)];
    double uEND = data[(i+1)+nx*((j+1)+ny* k)];
    double uWST = data[i    +nx*(j    +ny*(k+1))];
    double uEST = data[(i+1)+nx*(j    +ny*(k+1))];
    double uWNT = data[i    +nx*((j+1)+ny*(k+1))];
    double uENT = data[(i+1)+nx*((j+1)+ny*(k+1))];

    double posX = (coord_x - pWSD.x) ;
    double locX = posX / hx - i;
    double posY = (coord_y - pWSD.y);
    double locY = posY / hy - j;
    double posZ = (coord_z - pWSD.z);
    double locZ = posZ / hz - k;

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    //cout << "coord_locX locY locZ " << locX << " " << locY << " " << locZ << endl;

    if (uWSD == 0.0 || uESD == 0.0 || uWND == 0.0 || uEND == 0.0 || uWST == 0.0 || uEST == 0.0 || uWNT == 0.0 || uENT == 0.0)
    {
        std::vector<double> gradient = { 0.0 , 0.0 , 0.0};
        return gradient;
    }
    double uTOT(0);
    double uET, uWT, uWD, uED;
    double uT, uD, uN, uS, uW, uE;

    double uGradientZ, uGradientX, uGradientY;

    //assume: all values are != defaultInterpolation
    //does not hold for curved interfaces
    /*
    return uWSD * (1.0 - locX) * (1.0 - locY) * (1.0 - locZ) +
           uESD *        locX  * (1.0 - locY) * (1.0 - locZ) +
           uWND * (1.0 - locX) *        locY  * (1.0 - locZ) +
           uEND *        locX  *        locY  * (1.0 - locZ) +
           uWST * (1.0 - locX) * (1.0 - locY) *        locZ  +
           uEST *        locX  * (1.0 - locY) *        locZ  +
           uWNT * (1.0 - locX) *        locY  *        locZ  +
           uENT *        locX  *        locY  *        locZ;
    */
    uGradientX =    uWSD * (0.0 - 1.0) * (1.0 - locY) * (1.0 - locZ) +
                    uESD *        1.0  * (1.0 - locY) * (1.0 - locZ) +
                    uWND * (0.0 - 1.0) *        locY  * (1.0 - locZ) +
                    uEND *        1.0  *        locY  * (1.0 - locZ) +
                    uWST * (0.0 - 1.0) * (1.0 - locY) *        locZ  +
                    uEST *        1.0  * (1.0 - locY) *        locZ  +
                    uWNT * (0.0 - 1.0) *        locY  *        locZ  +
                    uENT *        1.0  *        locY  *        locZ;
    uGradientY =    uWSD * (1.0 - locX) * (0.0 - 1.0) * (1.0 - locZ) +
                    uESD *        locX  * (0.0 - 1.0) * (1.0 - locZ) +
                    uWND * (1.0 - locX) *        1.0  * (1.0 - locZ) +
                    uEND *        locX  *        1.0  * (1.0 - locZ) +
                    uWST * (1.0 - locX) * (0.0 - 1.0) *        locZ  +
                    uEST *        locX  * (0.0 - 1.0) *        locZ  +
                    uWNT * (1.0 - locX) *        1.0  *        locZ  +
                    uENT *        locX  *        1.0  *        locZ;

    uGradientZ =    uWSD * (1.0 - locX) * (1.0 - locY) * (0.0 - 1.0) +
                    uESD *        locX  * (1.0 - locY) * (0.0 - 1.0) +
                    uWND * (1.0 - locX) *        locY  * (0.0 - 1.0) +
                    uEND *        locX  *        locY  * (0.0 - 1.0) +
                    uWST * (1.0 - locX) * (1.0 - locY) *        1.0  +
                    uEST *        locX  * (1.0 - locY) *        1.0  +
                    uWNT * (1.0 - locX) *        locY  *        1.0  +
                    uENT *        locX  *        locY  *        1.0;
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    std::vector<double> gradient = {uGradientX / hx, uGradientY / hy, uGradientZ / hz};

    return gradient;

}

void PointInterpolator::smoothGrid()
{
    for (int i = 1 ; i < nx -1 ; i++)
    {
        for (int j = 1 ; j < ny -1 ; j++)
        {
            for (int k = 1 ; k < nz -1 ; k++)
            {
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                double div = 0;
                double sum = 0;
                if (data[i    +nx*(j    +ny* k)] != defaultInterpolation)
                {
                    sum += 2.0*data[i    +nx*(j    +ny* k)] ;
                    div++;div++;
                }
                if (data[i+1    +nx*(j    +ny* k)] != defaultInterpolation)
                {
                    sum += data[i+1    +nx*(j    +ny* k)] ;
                    div++;
                }
                if (data[i    +nx*(j +1   +ny* k)] != defaultInterpolation)
                {
                    sum += data[i    +nx*(j +1   +ny* k)] ;
                    div++;
                }
                if (data[i   +nx*(j    +ny* (k+1 ))] != defaultInterpolation)
                {
                    sum += data[i   +nx*(j    +ny* (k+1 ))] ;
                    div++;
                }
                if (data[i-1    +nx*(j    +ny* k)] != defaultInterpolation)
                {
                    sum += data[i-1    +nx*(j    +ny* k)] ;
                    div++;
                }
                if (data[i    +nx*(j -1   +ny* k)] != defaultInterpolation)
                {
                    sum += data[i    +nx*(j -1   +ny* k)] ;
                    div++;
                }
                if (data[i   +nx*(j    +ny* (k-1 ))] != defaultInterpolation)
                {
                    sum += data[i   +nx*(j    +ny* (k-1 ))] ;
                    div++;
                }
                if (div >0)
                {
                    data[i    +nx*(j    +ny* k)] =  sum / div;
                }
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            }
        }
    }
}

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void PointInterpolator::resetInterpolator()
{
    for (int iter = 0 ; iter < nx*ny*nz;iter++)
    {
        dataCounter[iter] = 0;
        data[iter] = defaultInterpolation;
    }
}

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void PointInterpolator::normToNumberOfWritings(bool p2norm)